During the process of designing electromagnetic components, such as the head or the motor of a magnetic recording device, a magnetic-field simulation is conducted to analyze the magnetic fields generated around any magnetic bodies, conductors, etc. In the magnetic-field simulation, a region to be analyzed is divided into small domains (hereinafter, “meshes”) and various equations are created to determine the magnetization state of each individual mesh. The behavior of the whole electromagnetic component when it is in a state of magnetization is predicted by solving the various created equations for the meshes as a set of simultaneous equations. A numerical analytical approach, such as the finite element method, is used to create and solve the simultaneous equations.
In an analysis according to the above-described numerical analytical approach using the finite element method, even spaces between the magnetic bodies and the conductors are divided into meshes. Various equations are then created to determine the magnetization states of the meshes in the interspaces. These equations, including the equations for the interspaces, are solved as a set of simultaneous equations. Accordingly, in the analysis according to the above-described numerical analytical approach using the finite element method, if the interspaces are deformed in accordance with movement of the magnetic bodies and the conductors, it is necessary to create new equations in accordance with the deformation and solve the new equations as a set of simultaneous equations. Such an analysis may take a long time.
The boundary element method is a well-known numerical analytical approach to magnetic-field simulation in which, even when the interspaces are deformed in accordance with movement of the magnetic bodies and the conductors, mesh generation of the deformed interspaces is not needed (see, for example, Japanese Laid-open Patent Publication No. 2006-18393 and Japanese Laid-open Patent Publication No. 2007-213384). More particularly, a numerical analytical approach using the boundary element method is a combination of the finite element method and the boundary element method. The magnetization state is analyzed where the individual magnetic bodies are moving in arbitrary directions. However, in the analysis according to the numerical analytical approach using the boundary element method, it is necessary to solve many simultaneous equations. Such an analysis may take a long time.
A numerical analytical approach using both the boundary integral method and the finite element method is known that does not need many simultaneous equations and thus can be used to efficiently simulate a magnetic field.
In an analysis according to this numerical analytical approach using both the boundary integral method and the finite element method, magnetic fields due to magnetization vectors in a magnetic body or similar and magnetic fields due to current vectors in a conductor or similar are calculated individually using the finite element method and the boundary integral method. An analysis method is known that analyzes the magnetization state using the calculated individual magnetic fields (see, for example, “Hybrid method for computing demagnetizing fields” IEEE transactions on Magnetics, vol. 26, No. 2, March (1990)). However, in an analysis according to the above-described numerical analytical approach, because scalar potentials are used to calculate the magnetic fields due to the magnetization vectors, it is impossible to take eddy currents into consideration that are caused by changes in relative positions between the magnetic bodies or caused by changes in the current over time.
Another numerical analytical approach using both the boundary integral method and the finite element method is known that takes the eddy currents into consideration (see, for example, “Three-dimensional micromagnetic finite element simulations including eddy currents”, J. Appl. Phys. 97, 10E311 (2005)).
However, in the analysis according to the above-described conventional technology, the effects of the magnetization vectors upon the magnetic field cannot be accurately considered. In the analysis according to the above-described conventional technology, the magnetic fields due to the current vectors in the conductor or similar are analyzed using the finite element method and the boundary integral method; however, the finite element method and the boundary integral method are not applicable to the equations that contain the magnetization vectors due to the magnetic body or similar. Therefore, the effects of the magnetization vectors upon the magnetic field cannot be accurately considered.
More particularly, in order to apply the finite element method and the boundary integral method to an equation, it is necessary to transform volume integrals on both sides of the equation into surface integrals; however, for the equations that contain the magnetization vectors, it is impossible to transform volume integrals into surface integrals. Therefore, the finite element method and the boundary integral method are not applicable to the equations that describe the magnetization vectors. As a result, in the analysis according to the above-described conventional technology, the effects of the magnetization vectors upon the magnetic field cannot be accurately considered.